1MA0 Higher June 2012 Paper 1 Q23
23
(a) Simplify fully \(\dfrac{x^2 + 3x - 4}{2x^2 - 5x + 3}\) (3)
(b) Write \(\dfrac{4}{x + 2} + \dfrac{3}{x - 2}\) as a single fraction in its simplest form. (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\dfrac{(x + 4)(x - 1)}{(2x - 3)(x - 1)}\) | \(\dfrac{x + 4}{2x - 3}\) | 3 | M1 for \((x + 4)(x - 1)\) M1 for \((2x - 3)(x - 1)\) A1 cao |
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\dfrac{4(x - 2)}{(x + 2)(x - 2)} + \dfrac{3(x + 2)}{(x + 2)(x - 2)}\) | \(\dfrac{7x - 2}{(x + 2)(x - 2)}\) | 3 | M1 for denominator \((x + 2)(x - 2)\) oe or \(x^2 - 4\) M1 for \(\dfrac{4(x - 2)}{(x + 2)(x - 2)}\) oe or \(\dfrac{3(x + 2)}{(x + 2)(x - 2)}\) oe (NB. The denominator must be \((x + 2)(x - 2)\) or \(x^2 - 4\) or another suitable common denominator) A1 for \(\dfrac{7x - 2}{(x + 2)(x - 2)}\) or \(\dfrac{7x - 2}{x^2 - 4}\) SC: If no marks awarded then award B1 for \(\dfrac{4(x - 2)}{x^2 - 2} + \dfrac{3(x + 2)}{x^2 - 2}\) oe |